Linear and non-linear learning

What is linear learning?

Some aspects of our educational system reflect its machine-age origins. If you look closely you will see the ethos of the factory: The textbooks, the curricula, the classrooms, and the schedules we follow. These are products of a 19th century factory model.

They haven’t changed much over the centuries. To this day, the bell rings and we take our places for 45 mins of instruction in neat rows. Then we receive mass-produced content that was designed around standardized tests - tests that do not accommodate individual learning needs.

The delivery model is that of the conveyor-belt. If the system is to work as a whole, the content has to be delivered in a very particular way: It has to be delivered in a linear format.

Textbook example

You can see the linear format at work in textbooks that stagger information: In most textbooks you're not supposed to proceed to Unit 2 until you’ve learned Unit 1. Nor will you will understand Unit 3 until you have ‘mastered’ Unit 2, and so on. Almost all textbooks are designed, literally, along such lines.

Let me give you an example from English language textbooks. For decades, they have traditionally begun with present tense (or aspect) verbs and usually with the 3rd person. He goes, and she eats, etc. These are commonly the first item in a long and linear sequence of items.

From there, the books invariably proceed to simple past tense, then past continuous, and then on to the perfect aspect, and so on. This is the order in which most newcomers to English meet the language. It's also an example of linear delivery.

Linear is arbitrary

The striking thing about the linear approach is how arbitrary it is. The sequences of language items I mentioned have nothing to do with how and when learners actually acquire the elements - still less to do with what they would encounter in the wild. The linear sequence is arbitrary.

It’s also the case that, in real life (and even in school life) learners of spoken English do not acquire the very first item of the entire sequence - the simple present tense - until they reach an advanced stage of fluency. The first will be last and there’s nothing the terxtbook writer can do about this.

So, it's interesting that Chinese speakers of English who have mastered many complex grammatical items continue to say “he go” rather than ‘ he goes’. For some reason the third persona singular 's' is a late acquired morpheme - in some cases very late. Again, this is the direct opposite of what textbook order suggests.

Expediency

The textbook sequence of items exists for reasons other than a natural order of learning. It's presented out of an order of teaching expediency. This qualifies as what we might call a teacher-centric approach.

One assumption behind the linear approach is, of course, that ‘if it is taught then the learning will follow’, regardless of any natural order of acquistion. That is problematic, to say the least.

Non-linear learning

So, what is non-linear learning? On one level, non-linear learning is the way that we naturally learned for a couple of hundred thousand years. In nature, linear learning doesn’t exist. People didn’t learn to swim or hunt in a linear way – through a staggered, textbook process. We learned instead by doing, through direct experience, through dealing with things as they arose, and through discovering what it was that was important at the time. But most of all, we learned through making connections between stuff we already knew and the stuff we didn't. This meant we actively constructed the knowledge as we needed it. It was all very subjective and individual and not linear.

In real life, children learn their mother tongue through random exposure. They make sense of the language by identifying patterns and they connect and store the patterns that work. Our brains are designed to work/learn this way, but it is a subjective process because each individual experiences distinct social and psychological phenomena. It is not an objective one size fit, but an experience that is entirely unique. Yet we all end up fluent in our native language.

Learning in the natural environment was not linear. There is a level on which it was actually quite random. It was situational.

Networks, not lines

If anything, non-linear learning has more to do with a network than a line. It's about experience and connecting the dots - in our distant past that meant remembering that a certain plant could be eaten, another could heal ilness, while others should be avoided, etc.

This type of learning has a neurological basis: Our neural networks form the basis of memory/knowledge and even the brain itself. The web, like the brain, is all about links and nodes. Its network qualities have massive implications for learning that I think we're just beginning to see. The rise of the web has meant the rise of a certain type of learning and it's based on a network of connections rather than on linear sequences.

This doesn’t mean we have to put an end to linear learning – far from it – but it does mean we have to be open to other possibilities, and the web is providing those. Networks are everywhere and, as Jay Cross persuasively argues, they are changing everything, including how we learn. The last time that happened we had the Enlightenment on our hands.

Writing techniques: Learning to write in a non-linear way

The problem with the a to z books on writing is that they suppress all context. Which means that each learner is forced to follow the book and jump through the same hoops, regardless of different needs.

If today’s lesson happens to be on the ‘split infinitive’ then the split infinitive it is and that’s what we do – end of discussion. As a learner, it means that the content has nothing to do with your life, your experience, or with anything you might actually want to learn. The effect is one-size-fits-nobody.

In order to combat the linearity problem, I’ve developed an approach that I call writing techniques. With writing techniques the learner is encouraged to develop first, her own interpretation of good writing. She is guided in how to ‘close read’ the texts to see the techniques below the surface that make it effective and she is presented with a number of techniques that are selected by the tutor as highly effective .

With enough skill in place to be able to make judgment calls, the learner is then encouraged to close read her own writing and find the gaps. The task then becomes to find out how acknowledged writers (from Gladwell to Chekov) solve his problems and learn from there. This approach subjective, connectivist, and non-linear.

Comments

I enjoyed our brief conversation on the topic this last Monday. In addition to my own language-learning experiences inside and outside the classroom, I’ve a bit of secondhand experience with the subject, as my mother homeschooled my younger brother after seeing all the fun I was having in the Philadelphia public school system. She was very heavily influenced by John Taylor Gatto, whose work isn’t really so much related to theories of education as it is to the social destruction wrought by institutionalized compulsory education, and by E.D. Hirsch’s “Core Knowledge” ideas and the “What Your [N]th-Grader Needs to Know” books, which relate somewhat to the ChinesePod model in that they posit a body of knowledge necessary for “cultural literacy” at various levels of development, but argue against prescribing any single way of acquiring it.

Language acquisition among children is a fascinating field of study, and one I wish I knew more about, but Mark Rosenfelder over at Zompist.com has an interesting piece on language acquisition as it relates to immigration debates — though I think it’s worth a look for anyone interested in the topic, at least if they’re as ignorant about it as I am.

When you visit a large city there is no way a “linear” approach can guide you to every place that might be possibly interesting. What do you want to see? A geeky little museum? A second-hand music shop? An alternative dance club? The medival fassades in the older parts of the city? The pubs serving freshly brewed local beer?

However, when you first enter the city you will be lost and probably miss the important stuff with a non-linear approach because you do not even know what is there and where to find it. Or worse: You run into dangerous areals late at night.

A good guided tour (appealing to your taste) that takes you to the vantage points and introduces you to the specialities of the city + tells you the do’s and don’t is gold. And the guided tour is of course a more or less “linear” approach.
After the tour you can explore the city according to your own interests, hobbies, and demands.

Oh and there might even be short linear phases coming up later, e.g. when you decide to explore the insect life of the city and do not know where to start.

The same is valid for other forms of knowledge acquisition:
When entering a new domain, nothing beats a good textbook that gives a structured (=linear) overview of the field, provides you with frameworks and maps, and warns you of the pitfalls. From there on a non-linear course is the way to go.

There are plenty of subjects that cannot be tackled with a non-linear approach, the most obvious being mathematics. There may be a variety of fields within maths, but without a rigourous attitude towards the basic principles, you will never master the subject. Indeed, most fields of mathematics can only be understood fully by starting from first principles. Maths will never be a subject where you can pick and choose what you want to learn and when.

I disagree – one can and does become fluent at language – mathematics is a language and fluency can be acquired in the same way in non linear fashion by putting the pieces together – the doing of maths is what is important for the non linear mind which I believe is what we all start out as but few survive because of the linear intensive programming

Brendan,
Language acquisition (though I think the term ‘acquisition’ is starting to look suspect) in kids is definitely a fascinating field and one I used to stay in touch with. Having read the Rosenfelder link, I think it’s time to revisit the topic.

Henning,
I just learned a new word – dichotomic! In fact, the two things are not mutually exclusive and your metaphor for visiting a city is entirely valid in certain contexts. The issue for me is control. Textbooks don’t act as brief intros to the cities of learning in most cases. They are the cities! Too often they are seen as the be-all and end-all of the learning. Far too many school kids just stick to the script and fail to discover the rest. This is my point.

Secondly, you and I probably have different tastes, preferences, needs, and learning styles. Who says there is to be only one guidebook to a vast city? Too often that ‘one-size-fits-none’ approach kills the interest of the learners, im my view. Fundamentally it robs the learner of choice and without some element of choice, I beleive learners will feel a lesser degree of commitment to the learning.

Natalie,
I disagree entirely. If your point was true then there would be only one way to learn math. Is there only one way to approach the basic principles of math? What are those principles and what is that one, true method? Has everyone in the world who learned math successfully taken the same route? Not at all, some of the greatest mathematician’s have been total mavericks who approached the subject in an entirely sujective and original way. Notice too that he greatest thinkers in these fields tend to work independently – not by following a script. My whole point about learnign is that the brain is designed to enable a wholly subjective approach to any subject as long as you have the motivation and the choice to choose, control, and direct the resources with some autonomy.

Ken,
A few semesters ago I helped create a Spanish language course for our nursing program here at UT Austin. It was amazing to see the different needs of the learners. Some worked with elderly, others with children. Some needed Spanish to talk to the parents of their patients, others worked in clinics, while some made home visits, etc. In the end we were able to give the students a lot of flexibility in how the class was structured. This was only possible by not forcing the issue of following a text book and a traditional syllabus. So I totally relate to your comments about the non-linear nature of learning.
On the other hand, I usually try to go cautious when comparing child L1 acquisition with adult L2. Even if we don’t totally accept brain lateralization, etc., there are still significant differences between how children and adults learn.
BTW, I’ll be in Shanghai in a couple of weeks. I already have an appointment to get with JP at SpanishPod, and I’ve also been talking with Steve Williams (I believe those are scheduled for Jan. 2). If you are in town, it would be a pleasure to talk shop with you too.
Orlando

I seem to find people who can learn under their own steam and people who can’t (a generalisation).

People who can are self-aware learners, they understand their own strengths and weaknesses and have spent sometime thinking about the learning process itself, basically they have aquired learning skills. Approaching a new learning problem they map previous experiances in learning to it and think about any unique issues. When they come to learn something they are looking for content, examples opportunities to practice and feedback etc.

People who can’t are looking for a course, a system, a map to an end point, a series of steps to take, a good teacher (nice, but how do you know how good your teacher is until you have spent sometime with them). If they fail they will blaim the course, system, map, teacher, etc.

Motivation is important but a motivated person may not know how to learn.

Depressingly even in the West, a lot of the people who know how to learn don’t seem to have aquired this ability at school, they aquired it afterwards. Surely by the time the majority of people leave school they should know how to learn (even if they choose not to).

Ken, I find myself at odds with some of the things you are saying here. Perhaps it is just a question of terms; we mean the same thing but say it in different ways. At times it may be because I am, in my own subjective way, hearing things you probably never meant to say. But now, belatedly, let me take a swing at what you had to say.

First, I get the feeling that you are saying that order and linear organization are the same thing. If so, I see that as a mistake. I find it hard to read, or to learn without some kind of apparent order (the first place I look in a book is the table of contents). Sometimes the order is a smoky link, sometimes it is an iron chain. But in looking at something we time-bound, social beings naturally try to discern an order or a meaning to things. As I see it the true opposite of order is random chance and I am sure that very few people wish to let wild chance alone govern what they learn.

Secondly, I feel the very best examples of learning opportunities are also wonderful examples of supremely ordered experiences or, shall we say, linear thinking (where a mind takes us in steps from one experience to the next). Literature and film follow a linear order in the sense that if you were to take out all the pages in a book and throw them in the air, by chance the result that lands on the table would almost certainly be much less satisfying than the original.

I see linearity as a journey. I see linearity as an order. And I see linearity as progression. I am entranced by each of these and how to use these to further learning. I hear nothing of these wondrous things in your musings and it “bugs” me because it is almost like you are trying to pull a Wizard of Oz and claim that what we are experiencing with web 2.0 is akin to magic when all along it is nothing but the wizard behind a new “networking” machine.

The opposite of linear order is chaos, chance and disorder and I don’t think you are serving any of these things up with Chinese-pod.

@micheal I am sure Ken has his own answer, but here is my take. I think there may just be a misunderstanding of terms but just in case.

I don’t think Ken is advocating total chaos and neither is web 2.0. I have seen an overly linear approach in education and it sucks, although of course there is always some level of progression (even if it is just that we will all age) otherwise how can you say you have learnt something.

If I wish to give directions to someone to visit me I can send them detailed instructions for every road and turning and distance they need to take. Great, unless they happen to make a single mistake or the route is changed by a diversion or something.

I can take a more holistic approach and start along the lines of “head for the West of the city first (there will be signs) then …. “. This is more robust
There may be variability in how people perform but most should be able to use the simple instructions to make their own way.

Finally I can recognise that technology is changing everything and knowing they have GPS in their car just send them my postcode and house number. Even if they want to internalise the information rather than just blindly follow the GPS I know they can go onto to Google maps to do this (they can even use the arial photos there to work out the quickest shortcut to pop out to a local shop for something whilst they are staying with me).

All of the above describe a journey and course of events that precede from start to finish (yes in some kind of linear fashion).

To my mind Ken is taking a shot at the education systems that are firmly embedded in example one, an approach that will work, so long as the students behave as predicted, so long as they think the same way that the person who writes down the instructions does and so long as the infrastructure does not change so that what I write today will still serve them well in five years time.

There is another point I would like to make, a more nebulous one, but yes there is a certain element of chaos, however in some chaotic systems you can still make assertions that something will happen depending on the probability of its occurrance and the size of the sample. In the traditional classroom I will interact with X number of fellow students, on the Web I can potentially connect with many more. I cannot gaurantee quality interaction either way but with the right tools I know which one my money is on. The same applies to the people that teach me etc. etc.

There are dangers, and in my poor attempt at an example they are probably best represented by the GPS system alone (in which the only only learning is to learn how to operate the equipment).

There is something new happening. Of I that I have no doubt. But can it be organized under the general rubric of non-linear? Of that I am profoundly sceptical.

I think Ken is an artist of sorts and that what he (and others at Praxis) is accomplishing is an art form. His artistry partakes of many disciplines but again I am profoundly sceptical that the “deep” organizing principle behind the Praxis educational experience is “non-linear” (whatever that means).

I am not an educationalist, but learner who feels I should spend more time looking at the learning process in order to learn better.

After a quick run through Google and the various materials I have gathered Ken’s use of “non-linear” seems to be entirely appropriate in this context (the earliest reference I found to non-linear language learning via the Web dates back to 1998). It seems that there is a strong precedent of the use of non-linear in Education to mean something like “not a single prescribed linear path” but rather a choice of many paths (which is not the same as chaos). This pleases me no end as that is exactly what I assumed and I was getting a little worried there for a minute.

As for the “deep” underlying organizing principle behind Praxis well I assume as a commercial organisation that is to make money (how deep do we want to go?). All I can say for sure is that I observed the original newbie lessons on Chinesepod (I know that is just a part of Praxis) originally start building in a linear, progressive manner and then delibrately switch to something that was much errr… is it safe to say “less linear” approach. There was also disscussion about this in the blogs and forum. I think we can therefore credit Praxis with some deliberate non-linear thinking.

So I guess for non-linear and its meaning we just need to follow and read some of those Google links and in this context it just means what most people think it means.

I’m sure my comment will sound rather uneducated and in layman’s terms compared to the others’ but I’ll have a go anyway. I would just like to say I know what you’re talking about Ken, with Chinesepod I have learned more in months than I ever have in 8 years of manadtory school French lessons! Keep up the excellent work.

I absolutely agree with you, but it strikes me that the success of ChinesePod depends not only on the structure of the lessons, but on the personal chemistry and charisma of you and Jenny Zhu. I’m a Newbie, just beginning to dip my toes into the Elementary level, and the few lessons I’ve listened to that don’t feature you and Jenny have lacked the spark that keeps me attentive otherwise.

Which leads me to that old chestnut: it’s not the method, the materials, the content—it’s the teacher. As a teacher myself, I would put it this way: if the teacher is inspired, he or she has a chance to inspire students. An inspired lecturer can thrill an audience of 300; an uninspired constructivist can kill the best designed lesson in a class of 15. Inspiration is the key—everything else is secondary.

Thanks so much for ChinesePod, which keeps me inspired to continue improving my Chinese!

Ken, while ChinesePod seems pretty good, I am not sure it is that revolutionary, or optimal, as you seem to think. I think it suffers from the same problem many other new-fanled methos of self-study suffer from. namely that it is too non-linear. That’s right, I said non-linear. But I mean it in a slightly different sense. The point is simply that the more linearly you progress from unit to unit, the easier it is to keep studying. In a classroom setting, it makes sense to have a textbook, tapes, quizes, conversations etc because you always have someone telling you what to do. Now in self-study, the biggest enemy is always, always your inherent lazyness. With enough motivation, you could learn any language with aid of just a dictionary, they are usually filled with phrases, rudimentary grammar and of course lots of words. The problem is that you don’t know where to start, so you probably give up before long. If instead you always have someone telling you what to do next, staying motivated (the one prerequisite for success) is so much easier. IF you supply the user with, say, five different ways to study and reinforce what they learnt, they will just get lost if they have to navigate between them on their own.

On the other hand, while I am personally very interested in theoretical grammar, I don’t think that teaching grammar is conducive to learning a language, other than indirectly. As long as you consciously decline and conjugate in your head before opening you mouth, you don’t really speak the language. The actual task you need to undertake is to reinforce patterns of speach, subconsciously associate certain tempora and grammatical persons with certain endings etc. But going by way of consciously learning and understanding (the simplified rules that we call) the grammar of the language is taking a long and completely unnecessary detour. Just look at children.

I didn’t make the claim that ChinesePod is either revolutionary or optimal. Not sure where that came from.

I think we’ve been all trained to ‘always have someone telling us what to do’, but I most certainly don’t think it has to be like that. Being told what to do isn’t very motivating for many people. But even more importantly, learner autonomy isn’t a nicety – we all have to become independent, autonomous learners in a future where there are terabytes of the data coming at us daily. We simply don’t have the luxury of waiting for the authorities somehwere to map out what we should be learning and then to push us into doing so. Those days are coming to and end.

Ah, I didn’t mean that you should be told what to do, rather how to do it. You have probably heard of Pimsleur and simlar courses on tape. While perhaps a bit boring at times, they have the very important advantage of not giving the learner an excuse to linger or get lost on the way, beacause you there is no room for choices at all. It is like weight training, the hard part is not lifting the weights, but being motivated, overcoming the psychological barriers. If you always know what comes next, it is much easier to keep going. Some people with particularly low motivation use personal trainers that tell them what to do.

Now I am not saying that the flow of the course should be predetermined, or not take the individual learner into account, I am just saying that you shouldn’t be presented with too many choices at each point. Ideally it should be like having a personal trainer, or a personal language coach. “So now that we have read this text, let’s practice writing the characters”. The user will otherwise be at loss, he will not be sure of how much time to put into each particular exercise, in which order to do them etc. This state of mind is very tiring, and will eventually lead to him quitting the course.

By the way, I don’t think that the vast majority of people are even interested in becoming autonomous, and I am not sure how a society of millions of creative bohemians would work. Certainly all societies to date have been based on a very large base of ordinary workers that don’t ask too many questions. But be that as it may, the question here only concerns how to produce an effective learning tool.

I see where you’re coming from but you’re kind of putting words into my mouth, as it were. I’m not aksing that we all become bohemians, or anything else. I’m suggesting that we have to become more autonomous, given the future that awaits us.

I totally agree that too much choice is overwhelming. That’s why w’ve tried to create learning ecosystems with ChinesePod/SpanishPod. These are designed to give guidance and context but also with as much freedom and choice to explore the language as possible – learning on your terms. The community, the practitioners, and the experience of others all provide guidance and motivation for the learners. I believe this works quite well over there and I beleive we will see more of this type of approach in the future.

To me, learning and teaching English (to my mainly Mexican ESL 4th graders) was somewhat easier than learning Hangeul (Korean). Many of the phonemes needed breif practice because it was a Roman alphabet, the spelling rules took 10 minutes, and we were able to review the grammar book 3 times before the year was over. I did not take the book approach of teaching all of the verbs first, then nouns, etc. For me personally, I did not see a system that way and it confused me. So I taught lesson one of each chapter (verbs, nouns, adj., etc) within the week in present I. Then we went back and discussed the simple forms and variations that could happen to each. The third time around we did the entire chapter. I got this method off Nihouse and I don’t know if to call it linear or circular but it made sense because I could see structure right away. Meaning had to be derived from reading (2 hour block) and practice was in the form of writing (1 hour block).
On the other hand, the Asian languages started rough. There was no way I could discern anything but the last word that they spoke and that was hard to commit to memory. Nothing like the Romance languages. I had to start with phonemes and learning how to “read.” If I could relate the sounds to a system than felt better situated. I don’t watch the lesson in sequential order, but according to the needs of the day. Overall, you have to put some work in so that a language becomes acquired and usuable,

I just read your paper and it’s excellent.I particularly liked the points about the Emphasis on Individual Learning Processes, and Teachers as Resources and Models. Your observations certainly square with my experience and they could apply in most any learning scenario. I would also be tempted to add some thoughts regarding the use of technology, and particularly the principles behind connectivism. (Since so much of our future learning will migrate to the web, I believe we need a pedagogy that tackles it.) My second instinct here is to ask how you apply this stuff. For me, it’s about embedding what we learn into the ecosystem, Community of Practice, or ‘learnscapes, whichever term you prefer.

Thanks a lot Carroll: I m an English teacher who positively believes in the non linear approach. I ve been a chaos theory researcher and so far I ve been applying non linear techs to facilitate the learning of Enlglish. Guess what ! after a five months English training period my students learn more , faster wihtin a non-squared and non book based learning than those of other teachers.For exmple, I may start a beginners class by helping students to learn the days of the week and maybe ,I may be starting talking about the weather and from that learn the time and from there to another kind of related topic and so on.

Thank goodness for this site here that I found and for the string of communication here. Why did these posts stop in 2008? This topic, this reality is very important. We have too many kids falling between the cracks that are non linear because of the linear approach. I’m not a big fan of technology but yes indeed think goodness for the internet. Thank God for Elaine Aron, Bill Harris, David Hawkins & you Ken.

You ask, how to improve the individual / humanity’s nonlinear thinking?

Answer — nonlinearize ecology — disregard those who linearly say, “white is the best color” — rather, replace 4 white walls substrate with a logical substrate like nature, i can give examples but a nonlinear Utopia is for humanity to devise:

[…] to consider materials that were available at this time etc. etc. Of course you could turn all this linear sequencing on its head and offer all weeks together, so that the students can access material that would be […]

[…] not just me saying this – the linear model has been criticized for being stuck in the Victorian era, when it was all about factory production lines. Individuality and creativity have been stifled by […]

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